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The Topology of Foliations Formed by the Generic K-Orbits of a Subclass of the Indecomposable MD5-Groups
The present paper is a continuation of [13], [14] of the authors.
Specifically, the paper considers the MD5-foliations associated to connected
and simply connected MD5-groups such that their Lie algebras have 4-dimensional
commutative derived ideal. In the paper, we give the topological classification
of all considered MD5-foliations. A description of these foliations by certain
fibrations or suitable actions of and the Connes' C*-algebras
of the foliations which come from fibrations are also given in the paper.Comment: 20 pages, no figur
Triangular de Rham Cohomology of Compact Kahler Manifolds
We study the de Rham 1-cohomology H^1_{DR}(M,G) of a smooth manifold M with
values in a Lie group G. By definition, this is the quotient of the set of flat
connections in the trivial principle bundle by the so-called gauge
equivalence. We consider the case when M is a compact K\"ahler manifold and G
is a solvable complex linear algebraic group of a special class which contains
the Borel subgroups of all complex classical groups and, in particular, the
group of all triangular matrices. In this case, we get a
description of the set H^1_{DR}(M,G) in terms of the 1-cohomology of M with
values in the (abelian) sheaves of flat sections of certain flat Lie algebra
bundles with fibre (the Lie algebra of G) or, equivalently, in terms
of the harmonic forms on M representing this cohomology
Spectral Properties of the Generalized Spin-Fermion Models
In order to account for competition and interplay of localized and itinerant
magnetic behaviour in correlated many body systems with complex spectra the
various types of spin-fermion models have been considered in the context of the
Irreducible Green's Functions (IGF) approach. Examples are generalized d-f
model and Kondo-Heisenberg model. The calculations of the quasiparticle
excitation spectra with damping for these models has been performed in the
framework of the equation- of-motion method for two-time temperature Green's
Functions within a non-perturbative approach. A unified scheme for the
construction of Generalized Mean Fields (elastic scattering corrections) and
self-energy (inelastic scattering) in terms of the Dyson equation has been
generalized in order to include the presence of the two interacting subsystems
of localized spins and itinerant electrons. A general procedure is given to
obtain the quasiparticle damping in a self-consistent way. This approach gives
the complete and compact description of quasiparticles and show the flexibility
and richness of the generalized spin-fermion model concept.Comment: 37 pages, Late
Relativistic effects in the solar EOS
We study the sensitivity of the sound speed to relativistic corrections of
the equation of state (EOS) in the standard solar model by means of a
helioseismic forward analysis. We use the latest GOLF/SOHO data for modes to confirm that the inclusion of the relativistic corrections to
the adiabatic exponent computed from both OPAL and MHD EOS leads to
a more reliable theoretical modelling of the innermost layers of the Sun.Comment: 3 pages, 3 figures, aa.cls, to appear on Astronomy and Astrophysic
Spin-oscillator model for DNA/RNA unzipping by mechanical force
We model unzipping of DNA/RNA molecules subject to an external force by a
spin-oscillator system. The system comprises a macroscopic degree of freedom,
represented by a one-dimensional oscillator, and internal degrees of freedom,
represented by Glauber spins with nearest-neighbor interaction and a coupling
constant proportional to the oscillator position. At a critical value of
an applied external force , the oscillator rest position (order parameter)
changes abruptly and the system undergoes a first-order phase transition. When
the external force is cycled at different rates, the extension given by the
oscillator position exhibits a hysteresis cycle at high loading rates whereas
it moves reversibly over the equilibrium force-extension curve at very low
loading rates. Under constant force, the logarithm of the residence time at the
stable and metastable oscillator rest position is proportional to as
in an Arrhenius law.Comment: 9 pages, 6 figures, submitted to PR
Nonequilibrium dynamics of a fast oscillator coupled to Glauber spins
A fast harmonic oscillator is linearly coupled with a system of Ising spins
that are in contact with a thermal bath, and evolve under a slow Glauber
dynamics at dimensionless temperature . The spins have a coupling
constant proportional to the oscillator position. The oscillator-spin
interaction produces a second order phase transition at with the
oscillator position as its order parameter: the equilibrium position is zero
for and non-zero for . For , the dynamics of
this system is quite different from relaxation to equilibrium. For most initial
conditions, the oscillator position performs modulated oscillations about one
of the stable equilibrium positions with a long relaxation time. For random
initial conditions and a sufficiently large spin system, the unstable zero
position of the oscillator is stabilized after a relaxation time proportional
to . If the spin system is smaller, the situation is the same until the
oscillator position is close to zero, then it crosses over to a neighborhood of
a stable equilibrium position about which keeps oscillating for an
exponentially long relaxation time. These results of stochastic simulations are
predicted by modulation equations obtained from a multiple scale analysis of
macroscopic equations.Comment: 30 pages, 9 figure
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